自由漂浮空间机器人路径优化的Legendre伪谱法

基于Legendre 伪谱法研究自由漂浮空间机器人非完整路径规划的最优控制问题. 自由漂浮是空间机器人执行任务常用的工作模式，其路径优化是空间机器人完成复杂空间任务的基础. 由于空间机器人不具有固定基座，机械臂和载体之间存在非完整约束，使得自由漂浮空间机器人路径规划完全不同于地面机器人而变得具有挑战性. 本文提出自由漂浮空间机器人路径规划的最优控制伪谱方法. 首先，利用多体动力学理论建立自由漂浮空间机器人动力学模型，给定系统的初始和目标位形，选取机械臂关节耗散能最小为性能指标，并考虑实际控制输入受限，建立其路径规划的Bolza 问题. 然后，应用Legendre 伪谱法，将状态和控制变量在Legendre-Gauss-Lobatto (LGL) 点上离散，并构造Lagrange 插值多项式逼近系统状态和控制变量，将连续路径优化问题离散化为非线性规划问题求解. 最后通过数值仿真表明，应用Legendre 伪谱法求解自由漂浮空间机器人非完整路径规划问题，得到的机械臂和载体最优运动轨迹，较好地满足各种约束条件，且计算精度高、速度快，并具有良好的实时性. 

PATH PLANNING OF FREE FLOATING SPACE ROBOT USING LEGENDRE PSEUDOSPECTRAL METHOD

Based on the Legendre pseudospectral method, the optimal control of free floating space robots path planning problems are studied. Free floating is the working status for the space robots in task and path planning is the foundation for them to fulfil a complex space task. Because the space robots have no fixed pedestal and there are nonholonomic constraints between the manipulator and the carrier, and it makes the path planning for free floating space robots different from those on the ground. In this paper, the Legendre pseudospectral method which can realize the optimal control of free floating space robots path planning problem is presented. Firstly, a dynamic model of free floating space robots is estab-lished by using multi-body dynamics theory. The path planning problem of Bolza with certain initial and terminal stance is then obtained. Here, we select the minimum joint dissipation as performance index and consider the actual control input saturation. Then, by applying the Legendre pseudospectral method, the state and control variables are discretized at Legendre-Gauss-Lobatto (LGL) point and Lagrange interpolation polynomials are constructed to approximate the state and control variables. The problem of continuous path optimization is discretized to solve a nonlinear programming prob-lem. Finally, results of the numerical simulation show that using the application of Legendre pseudospectral method to solve the problem of free floating space robot path planning can get the optimal trajectory of manipulator and carrier. It can fit various constraint conditions well. And this method is with fast simulation calculation, high accuracy and good real-time performance.